Alfvén Wave Speed Calculator

An Alfvén wave is a low-frequency magnetohydrodynamic (MHD) wave in a magnetized plasma, where the magnetic field lines act like tensioned strings and the plasma's mass provides inertia, allowing transverse disturbances to propagate along the field. It is named after Hannes Alfvén, who first described this wave mode and later won the Nobel Prize in Physics partly for this work.

v_A = B / √(μ₀ρ), where B is the magnetic field strength, μ₀ is the vacuum permeability, and ρ is the plasma mass density (dominated by ions). It is directly analogous to the speed of a wave on a string, v = √(tension/mass per length), with magnetic tension playing the role of string tension.

Ions are thousands of times more massive than electrons, so even though both species contribute equally to the plasma's charge density, the ions dominate the plasma's mass density (and therefore its inertia) almost completely. This is why Alfvén speed calculations use ion density and ion mass rather than electron properties.

In a tokamak fusion plasma, Alfvén speed is typically around 10 million metres per second, a few percent of the speed of light. In the much sparser but still strongly magnetized solar corona, Alfvén speed can be even higher, while in the tenuous solar wind it drops to tens of kilometres per second.

Alfvén speed sets the natural timescale for how quickly magnetic disturbances, like those from a solar flare or coronal mass ejection, propagate through a magnetized plasma. It is a key parameter in magnetic reconnection theory, magnetospheric physics, and understanding how energy moves through the solar wind and Earth's magnetosphere.

Alongside the Alfvén speed, magnetized plasmas support fast and slow magnetosonic waves, which combine the magnetic (Alfvén) and acoustic (sound) restoring forces at different angles relative to the field. Alfvén waves themselves are purely transverse and do not compress the plasma, unlike the magnetosonic modes.

In a formula sense, yes, if the density is low enough and the field strong enough, but this signals that the non-relativistic MHD approximation has broken down. Real physical Alfvén waves in tenuous, highly magnetized plasmas (like parts of the magnetosphere) can approach a significant fraction of the speed of light, requiring a relativistic MHD treatment beyond this basic formula.

Deuterium (an isotope of hydrogen with one proton and one neutron) is the leading fuel candidate for magnetic confinement fusion reactors, so its ion mass is a useful preset alongside ordinary hydrogen (protons) for fusion-relevant Alfvén speed calculations.

Not directly, the basic Alfvén speed formula depends only on magnetic field strength and mass density, not on temperature or thermal pressure. Temperature enters indirectly through the plasma beta parameter, which compares thermal to magnetic pressure and determines how much the Alfvén-wave picture is modified by pressure effects.

Alfvén wave speed measurements are used to diagnose plasma density and magnetic field strength in fusion devices and space plasmas, and Alfvén wave heating (driving waves at frequencies resonant with the plasma's natural Alfvén frequencies) is an active area of fusion plasma heating research.